To have a global negative population growth rate could only happen in the case of a severe epidemic, something like the Spanish Flu did a 100 years ago (~100s of million died then).
This would not really be good for anyone.
> To have a global negative population growth rate could only happen in the case of a severe epidemic
Why? Europe (as an example) has a net population decrease, why can't this happen on a global scale without an epidemic?
This presupposes that humanity is better off with fewer humans. I am far from convinced that this is the case.
Are you suggesting we should annihilate the human race altogether?